It is possible to execute the iProperties command from the API. The following VBA code will do it. However, it's not possible to set it to the Custom tab once the dialog is displayed.
Public Sub StartiPropertiesCommand() Dim controlDefs As ControlDefinitions Set controlDefs = ThisApplication.CommandManager.ControlDefinitions Select Case ThisApplication.ActiveDocument.DocumentType Case kAssemblyDocumentObject controlDefs.Item("AssemblyiPropertiesCmd").Execute Case kPartDocumentObject controlDefs.Item("PartiPropertiesCmd").Execute Case kDrawingDocumentObject controlDefs.Item("DrawingiPropertiesCmd").Execute Case kPresentationDocumentObject controlDefs.Item("PresentationiPropertiesCmd").Execute End Select End Sub
To learn more about directly running Inventor commands see:
http://modthemachine.typepad.com/my_weblog/2009/03/running-commands-using-the-api.html
This just executes the command, the same as if you run the command in the UI. It's not possible to set the tab through the API. It might be possible using the Windows API, but that wouldn't be simple.